The N-dimensional quantum Hamiltonian (H) over cap =-h(2)vertical bar q vertical bar/2(eta +vertical bar q vertical bar del(2) - k/eta + vertical bar q vertical bar is shown to be exactly solvable for any real positive value of the parameter eta. Algebraically, this Hamiltonian system can be regarded as a new maximally superintegrable eta-deformation of the N-dimensional Kepler-Coulomb Hamiltonian while, from a geometric viewpoint, this superintegrable Hamiltonian can be interpreted as a system on an N-dimensional Riemannian space with nonconstant curvature. The eigenvalues and eigenfunctions of the model are explicitly obtained, and the spectrum presents a hydrogen-like shape for positive values of the deformation parameter eta and of the coupling constant k.

Ballesteros, A., Enciso, A., Herranz, F.j., Ragnisco, O., Riglioni, D. (2013). A maximally superintegrable deformation of the N-dimensional quantum Kepler-Coulomb system. In XXIST INTERNATIONAL CONFERENCE ON INTEGRABLE SYSTEMS AND QUANTUM SYMMETRIES (ISQS21); JOURNAL OF PHYSICS. CONFERENCE SERIES. BRISTOL : IOP Publishing [10.1088/1742-6596/474/1/012008].

A maximally superintegrable deformation of the N-dimensional quantum Kepler-Coulomb system

RAGNISCO, Orlando;
2013-01-01

Abstract

The N-dimensional quantum Hamiltonian (H) over cap =-h(2)vertical bar q vertical bar/2(eta +vertical bar q vertical bar del(2) - k/eta + vertical bar q vertical bar is shown to be exactly solvable for any real positive value of the parameter eta. Algebraically, this Hamiltonian system can be regarded as a new maximally superintegrable eta-deformation of the N-dimensional Kepler-Coulomb Hamiltonian while, from a geometric viewpoint, this superintegrable Hamiltonian can be interpreted as a system on an N-dimensional Riemannian space with nonconstant curvature. The eigenvalues and eigenfunctions of the model are explicitly obtained, and the spectrum presents a hydrogen-like shape for positive values of the deformation parameter eta and of the coupling constant k.
Ballesteros, A., Enciso, A., Herranz, F.j., Ragnisco, O., Riglioni, D. (2013). A maximally superintegrable deformation of the N-dimensional quantum Kepler-Coulomb system. In XXIST INTERNATIONAL CONFERENCE ON INTEGRABLE SYSTEMS AND QUANTUM SYMMETRIES (ISQS21); JOURNAL OF PHYSICS. CONFERENCE SERIES. BRISTOL : IOP Publishing [10.1088/1742-6596/474/1/012008].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/174389
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